{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 Crank-Nicolson Scheme\n",
    "\n",
    "In Listing 3\n",
    "\n",
    "```\n",
    "beta: (alpha*dt)/(2*dx*dx)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x_l, x_r, t = -1, 1, 1\n",
    "dx, dt = 0.025, 0.025\n",
    "nx = int((x_r - x_l) / dx)\n",
    "nt = int(t / dt)\n",
    "\n",
    "alpha = 1 / np.pi**2\n",
    "# pay attention to the beta\n",
    "beta = 0.5 * alpha * dt / dx**2\n",
    "\n",
    "u = np.zeros((nt + 1, nx + 1))\n",
    "x = np.linspace(x_l, x_r, nx+1)\n",
    "\n",
    "u[0, :] = -np.sin(np.pi*x, dtype=np.double)\n",
    "u[0, 0], u[0, -1] = 0, 0\n",
    "\n",
    "a = [-beta] * (nx-1) + [0]\n",
    "b = [1] + [1.0 + 2 * beta] * (nx-1) + [1]\n",
    "c = [0] + [-beta] * (nx-1)\n",
    "for i in range(1, nt+1):\n",
    "    d = [0] + [beta * u[i-1, j+1] + (1 - 2 * beta) * u[i-1, j] + beta * u[i-1, j-1] for j in range(1, nx)] + [0]\n",
    "    A = np.diag(b,0) + np.diag(a,-1) + np.diag(c,1)\n",
    "    u[i, :] = np.linalg.solve(A, d)\n",
    "u_ref = -np.exp(-t) * np.sin(np.pi * x)\n",
    "error = np.abs(u_ref - u[-1, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4), dpi=100)\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(x, u_ref, \"k-\", linewidth=1.0, label=\"Solution\")\n",
    "plt.scatter(x, u[-1, :], facecolor=\"none\", edgecolor=\"blue\", s=20, linewidths=0.5, label=\"CN\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"$u$\")\n",
    "plt.title(\"Solution field\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x, error, facecolor=\"none\", edgecolor=\"red\", s=20, linewidths=0.5)\n",
    "plt.ylabel(r\"$\\epsilon$\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.title(\"Discretization error\")\n",
    "plt.tight_layout()\n",
    "plt.ticklabel_format(axis='y', style='sci', scilimits=(-4,-4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "gpytorch",
   "language": "python",
   "name": "gpytorch"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
